# Tukey's symmetrical lambda distribution

U ~ Uniform(0,1)

$$Z_\lambda = \frac{U^\lambda-{(1-U)}^\lambda}{\lambda}$$

I have to find the first four moments and two ($\lambda_1,\lambda_2$) such that they have the same four moments.

• What are $\lambda_1$ and $\lambda_2$? – wolfies Apr 16 '16 at 17:23
• The odd moments are zero. What are you going to do with the first 4 moments? And what are the constraints on parameter $\lambda$? – wolfies Apr 16 '16 at 17:27
• I have the same question is on Introduction to the Theory of Statistic _Mood Graybill and Boes_1974 chapter III question 30 I appreciate some help. – Luis M Martin Alvarez Apr 18 at 17:39